Categorisation by Class: Tetragonal

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• Jon Goss
• AIMPRO

Cubic			(T Th O Td Oh)
Tetragonal
Operations	Order	Schönflies Symbol	International Symbol	Full Symmetry Symbol	Correlation Table	Irred. Rep. products	x i	Isomorph. with
E, C4, C2, C43	4	C4	4	4			C4h	S4
E, S4, C2, S43	4	S4					C4h	C4
E, C4, C2, C43, i, S43,h, S4	8	C4h	4/m				C4h
E, 2C4, C2, 2C2’, 2C2’’	8	D4	422	422			D4h	C4v, D2d
E, 2C4, C2, 2v, 2d	8	C4v	4mm	4mm			D4h	D4, D2d
E, 2S4, C2, 2C2’, 2d	8	D2d(Vd)	2m	2m			D4h	D4, C4v
E, 2C4, C2, 2C2’, 2C2’’, i, 2S4,h, 2v, 2d	16	D4h	4/mmm				D4h
Orthorhombic			(D2 C2v D2h)
Monoclinic			(C2 Cs C2h)
Triclinic			(C1 Ci)
Trigonal			(C3 S6 D3 C3v D3d)
Hexagonal			(C6 C3h C6h D6 C6v D3h D6h)
Non-crystallographic			(C Ch Cv Dh C5 S8 D5 C5v C5h D4d D5d D5h D6d I Ih)
All

This table lists point group symmetries along with their symmetry operations, the order of the group (i.e. the number of symmetry operations) and common notations.links to a correlation table, andlinks to tables of products of irreducible representations. The group produced by combination with inversion is listed under "x i". This, in the case of crystolographic point groups, is the Laue class which corresponds to the symmetry of reciprocal space. Isomorphic groups are also listed where character tables are available.